12-05: Trigonometric Equations

Trigonometric Functions

• Periodic function: a function where the y values repeat over regular x value intervals

Key properties

y = sinx

y = cosx

y = tanx

Properties of Secondary Trig Functions

y = cscx

y = secx

y = cotx

Transformations of Sine and Cosine

Graphing Sine and Cosine Functions

Mapping

(x,y) → (1/k x - p, ay + q)

Average (sine), Max (cosine), Average, Min

Properties (Graph with x and y scale)

y-scale

avg = q

max = q + |a|

min = q - |a|

x-scale

period = 2π / k

QI (quarter intervals) = Period/4

avg (Sin), max (Cos), avg, min, (and so on)

Solving Trigonometric Equations

Strategies

1. Rearrange (isolate for trig ratio)

2. Factor (exponents, same ratios repeats)

3. Identities (multiple ratios)

   • CAST rule must always be considered

   

Solving for Angles:

Solving Trigonometric Equations

Strategies

1. Rearrange - isolate for trig ratios
2. Factor - exponents, same ratio repeats
3. Identities - multiple ratios

In all cases: must consider CAST rule

Applications and IROC

AROC: average rate of change - slope of secant of curve

IROC: instantaneous rate of change - slope of tangent line (+ and - 0.001)

slope = ∆y/∆x

slope =( y2 - y1)/(x2 - x1)